Answer:
8 feet
Step-by-step explanation:
First, draw a picture. The pole is 22 feet tall. Katherine is 5.5 feet tall. She is 24 feet from the pole. The light from the top of the pole to the tip of her shadow forms two similar right triangles. The length of her shadow is x.
Now use similar triangles to write a proportion:
22 / (24 + x) = 5.5 / x
Cross multiply:
22x = 5.5 (24 + x)
Distribute:
22x = 132 + 5.5x
Combine like terms:
16.5x = 132
Divide:
x = 8
The shadow is 8 feet long.
Obtuse triangle, if the two angles add up to 50 degrees and a whole triangle equals 180 degrees. That means the third angle is greater than 90 degrees and only obtuse angles are greater than 90 degrees
Answer: it’s the first 1
Step-by-step explanation:
Answer:
<em>The domain of f is (-∞,4)</em>
Step-by-step explanation:
<u>Domain of a Function</u>
The domain of a function f is the set of all the values that the input variable can take so the function exists.
We are given the function

It's a rational function which denominator cannot be 0. In the denominator, there is a square root whose radicand cannot be negative, that is, 4-x must be positive or zero, but the previous restriction takes out 0 from the domain, thus:
4 - x > 0
Subtracting 4:
- x > -4
Multiplying by -1 and swapping the inequality sign:
x < 4
Thus the domain of f is (-∞,4)

If
, then we can immediately cancel the factors of
:

Factorize the numerator and denominator:


Next, if
, then
